Finite Group Databasebeta

← C2×#10594206 #11901504

Subgroups — C2×#10594206 #11901504

Order 1152.

2733 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×#884C211yesmaximal, characteristic, complemented
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63971C211yesmaximal, characteristic, complemented
7C2×#63958C211yesmaximal, characteristic, complemented
8C2×#63911C211yesmaximal, characteristic, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63897C211yesmaximal, characteristic, complemented
11C2×#63884C211yesmaximal, characteristic, complemented
12C2×#63880C211yesmaximal, characteristic, complemented
13C2×#63867C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594206C2116yesmaximal, direct product factor
17C2×#5615—31nomaximal
18C2×#5535—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37#64093C2218yescomplemented
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#884C2218yescomplemented
46C3×#877C2218yescomplemented
47#63978C2218yescomplemented
48#63978C2218yescomplemented
49#63971C2218yescomplemented
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60#63958C2218yescomplemented
61#63911C2218yescomplemented
62C4×#626C2218yescomplemented
63#63897C2218yescomplemented
64#63884C2218yescomplemented
65#63880C2218yescomplemented
66#63867C2218yescomplemented
67#63853C2218yescomplemented
68#63850C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#117—31no—
71C2×#940—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#938—31no—
76C2×#935—31no—
77C2×#930—31no—
78C2×#930—31no—
79C2×#929—31no—
80C2×C4×#67—31no—
81#5615—316no—
82#5535—316no—
83C2×#894—31no—
84C2×#894—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#889—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—61no—
94C2×#884D311yescharacteristic, complemented
95C2×#883—31no—
96C2×#67⋊C4—31no—
97C2×#877D311yescharacteristic, complemented
98C2×#874—31no—
99C2×C4×D12—31no—
100C2×C4×D12—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C2×#638—42no—
110C2×#638—42no—
111C2×#638C2314yes—
112C2×#638C2314yes—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4⋊(C3⋊D3)—42no—
116C2×C4⋊(C3⋊D3)C2314yes—
117C2×C4×C3⋊D3—42no—
118C2×C4×C3⋊D3C2314yes—
119C2×C3×#67—42no—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3—24no—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—42no—
132C2×C3×D12C2314yes—
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yes—
135C2×#626—24no—
136C2×#626—24no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#624—42no—
144C2×#624C2314yes—
145C2×D3×Dic3—42no—
146C2×D3×Dic3C2314yes—
147C32×C22⋊C4C2314yes—
148#3752C2314yes—
149#3750C2314yes—
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2314yes—
156C3×C4×Dic3C2314yes—
157#3724C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161#3722C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167C2×#540—91noSylow
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—61no—
182C22×#67—61no—
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C23×Dic3—31no—
186C23×Dic3C2×D311yescharacteristic
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—31no—
192C22×D12—31no—
193C22×D12—61no—
194C22×D12C2×D311yescharacteristic
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3C2×D311yescharacteristic
202C3×#121—38no—
203C3×#117—38no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C22⋊C4—21no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C22⋊C4C2×D311yescharacteristic
212C2×C3×C42—31no—
213C2×C3×C42—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217C2×D311yescharacteristic
218#940—38no—
219#939—38no—
220#939—38no—
221#939—38no—
222#938—38no—
223#935—38no—
224#930—38no—
225#930—38no—
226#929—38no—
227C4×#67—38no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—61no—
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—61no—
252C2×Dic3⋊C4C2×D311yescharacteristic
253C2×Dic3⋊C4C2×D311yescharacteristic
254C2×Dic3⋊C4C2×D311yescharacteristic
255C2×C4×Dic3C2×D311yescharacteristic
256C2×C4×Dic3C2×D311yescharacteristic
257#894—38no—
258#894—38no—
259#894—38no—
260#894—38no—
261#894—38no—
262#889—38no—
263#884—38no—
264#884—38no—
265#884—38no—
266#884—38no—
267#884—68no—
268#884C2×D318yescomplemented
269#883—38no—
270#67⋊C4—38no—
271#877C2×D318yescomplemented
272#874—38no—
273C4×D12—38no—
274C4×D12—38no—
275#870—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3C2412yes—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4C2412yes—
300C2×C32×C4C2412yes—
301#638—44no—
302#638—44no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307C4⋊(C3⋊D3)—44no—
308C4×C3⋊D3—44no—
309C3×#67—44no—
310C3×#67—44no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—28no—
317C2×C3×Dic3#4114yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C3×D12—44no—
325C3×C4×D3—44no—
326#626—28no—
327#626—28no—
328#626—44no—
329#626—44no—
330#624—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—91no—
334C2×#125—91no—
335C2×#123—91no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—31no—
340C2×#121—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#121—91no—
345C2×C4×D4—91no—
346C2×C4×D4—91no—
347C2×#117—31no—
348C24×C3—21no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3C22×D311yescharacteristic
360C23×D3C22×D311yescharacteristic
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—122no—
365C2×C3×D4—122no—
366C2×C3×D4—122no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—34no—
376C22×C3×C4—34no—
377C22×C3×C4—64no—
378C22×C3×C4—122no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—34no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—42no—
392C2×#67—42no—
393C2×#67—64no—
394C2×#67—64no—
395C2×#67—64no—
396C2×#67—64no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—124no—
404C2×#67—124no—
405C2×#67C22×D314yes—
406C2×#67C22×D314yes—
407C22×Dic3—24no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—34no—
413C22×Dic3—61no—
414C22×Dic3—61no—
415C22×Dic3—122no—
416C22×Dic3C22×D314yes—
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C2×D12—34no—
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—34no—
427C2×D12—34no—
428C2×D12—34no—
429C2×D12—42no—
430C2×D12—64no—
431C2×D12—64no—
432C2×D12—64no—
433C2×D12—122no—
434C2×D12—122no—
435C2×D12—124no—
436C2×D12—122no—
437C2×D12—122no—
438C2×D12C22×D314yes—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—34no—
444C2×C4×D3—42no—
445C2×C4×D3—64no—
446C2×C4×D3—122no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×C4×D3—122no—
450C2×C4×D3—124no—
451C2×C4×D3—122no—
452C2×C4×D3C22×D314yes—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C22⋊C4—24no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4C22×D314yes—
460C3×C22⋊C4C22×D314yes—
461C3×C42—34no—
462C3×C42—34no—
463#217—34no—
464#217—34no—
465#217—34no—
466#217C22×D314yes—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—64no—
479(C2×D3)⋊C4C22×D314yes—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D314yes—
492Dic3⋊C4C22×D314yes—
493Dic3⋊C4C22×D314yes—
494C4×Dic3C22×D314yes—
495C4×Dic3C22×D314yes—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—44no—
500C22×C32C2×#4112yes—
501C22×C32H(5,𝔽2)12yes—
502C22×C32H(5,𝔽2)12yes—
503C22×C32C2511yescharacteristic
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—44no—
511C2×C3⋊D3—44no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520C32×C4—22no—
521C32×C4—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3C2×#4114yes—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—31no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—31no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#127—98no—
546#125—98no—
547#123—98no—
548#123—98no—
549#123—98no—
550#123—98no—
551#121—38no—
552#121—98no—
553#121—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557C4×D4—98no—
558C4×D4—98no—
559#117—38no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C4⋊C4—91no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4D3211yescharacteristic
578C2×C42—31no—
579C2×C42—31no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—21no—
588C23×C3—32no—
589C23×C3—32no—
590C23×C3—42no—
591C23×C3—42no—
592C23×C3—42no—
593C23×C3—62no—
594C23×C3—62no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3C23×D312yes—
600C23×C3C23×D312yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C23×D311yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—64no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×D4—124no—
636C3×D4—124no—
637C3×D4—124no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—34no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—42no—
652C2×C3×C4—42no—
653C2×C3×C4—68no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—124no—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664#67—44no—
665#67—44no—
666#67—68no—
667#67—68no—
668#67—124no—
669#67—124no—
670#67—124no—
671#67—124no—
672#67—124no—
673#67—124no—
674#67—128no—
675#67—128no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—28no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—64no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—122no—
694C2×Dic3—124no—
695C2×Dic3#23514yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702D12—44no—
703D12—68no—
704D12—68no—
705D12—124no—
706D12—124no—
707D12—128no—
708D12—124no—
709D12—124no—
710C4×D3—44no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—128no—
716C4×D3—124no—
717C2×C32—42no—
718C2×C32#54014yescomplemented
719C2×C32C22×#4111yescharacteristic
720C2×C32C2×H(5,𝔽2)11yescharacteristic
721C2×C32C2×H(5,𝔽2)11yescharacteristic
722C3⋊D3—42no—
723C3⋊D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—91no—
729C24—91no—
730C24C2×D3211yescharacteristic
731C2×D4—34no—
732C2×D4—34no—
733C2×D4—34no—
734C2×D4—94no—
735C2×D4—94no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—122no—
742C2×D4—122no—
743C2×D4—122no—
744C2×D4—184no—
745C2×D4—184no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C2×D4—362no—
750C2×D4—362no—
751C22×C4—31no—
752C22×C4—34no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—34no—
759C22×C4—64no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—94no—
765C22×C4—122no—
766C22×C4—362no—
767C22×C4—362no—
768C22×C4—362no—
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—34no—
772C4⋊C4—34no—
773C4⋊C4—34no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4C2×D3214yes—
789C42—34no—
790C42—34no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—21no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—44no—
805C22×C3—44no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—84no—
813C22×C3—124no—
814C22×C3—124no—
815C22×C3C2×#23512yes—
816C22×C3#100412yes—
817C22×C3#100412yes—
818C22×C3D3×#4112yes—
819C22×C3#100912yes—
820C22×C3#100912yes—
821C22×C3C24×D311yescharacteristic
822C22×C3C24×D311yescharacteristic
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—44no—
830C2×D3—44no—
831C2×D3—64no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—128no—
850C2×D3—124no—
851C2×D3—124no—
852C2×D3—124no—
853C2×D3—124no—
854C2×D3—244no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—34no—
860C3×C4—42no—
861C3×C4—42no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865C3×C4—62no—
866C3×C4—62no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—22no—
871Dic3—22no—
872Dic3—64no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—62no—
877Dic3—122no—
878Dic3C2×#23514yes—
879C32C2×#54011yescharacteristic, complemented, Sylow
880C23—22no—
881C23—22no—
882C23—22no—
883C23—32no—
884C23—32no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—92no—
892C23—92no—
893C23—182no—
894C23—182no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23—182no—
899C23C22×D3212yes—
900C23C22×D3211yescharacteristic
901D4—124no—
902D4—124no—
903D4—124no—
904D4—188no—
905D4—188no—
906D4—364no—
907D4—364no—
908D4—364no—
909D4—364no—
910D4—364no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—34no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—68no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—92no—
927C2×C4—92no—
928C2×C4—124no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—364no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4C22×D3212yes—
935C2×C4C22×D3212yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—24no—
940C2×C3—42no—
941C2×C3—42no—
942C2×C3—82no—
943C2×C3—122no—
944C2×C3—122no—
945C2×C3#553514yescomplemented
946C2×C3#561514yescomplemented
947C2×C3C22×#23511yescharacteristic
948C2×C3C2×#100411yescharacteristic
949C2×C3C2×#100411yescharacteristic
950C2×C3C2×D3×#4111yescharacteristic
951C2×C3C2×#100911yescharacteristic
952C2×C3C2×#100911yescharacteristic
953D3—42no—
954D3—42no—
955D3—124no—
956D3—122no—
957D3—122no—
958D3—122no—
959D3—122no—
960D3—242no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—44no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—124no—
972C22—124no—
973C22—182no—
974C22—182no—
975C22—182no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—364no—
980C22—364no—
981C22D3×#23512yes—
982C22#6431412yes—
983C22#6431412yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—22no—
987C4—34no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—62no—
993C4—182no—
994C4—182no—
995C3—21no—
996C3C2×#553511yescharacteristic, complemented
997C3C2×#561511yescharacteristic, complemented
998C2—42no—
999C2—122no—
1000C2—122no—
1001C2—362no—
1002C2—362no—
1003C2#1059420614yesdirect product factor
1004C2C2×D3×#23511yescharacteristic
1005C2C2×#6431411yescharacteristic
1006C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#64093C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#877C2semidirect
4. C2×#63978C2semidirect
5. C2×#63978C2semidirect
6. C2×#63971C2semidirect
7. C2×#63958C2semidirect
8. C2×#63911C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63897C2semidirect
11. C2×#63884C2semidirect
12. C2×#63880C2semidirect
13. C2×#63867C2semidirect
14. C2×#63853C2semidirect
15. C2×#63850C2semidirect
16. #10594206C2direct (N × H)
37. #64093C22semidirect
45. C3×#884C22semidirect
46. C3×#877C22semidirect
47. #63978C22semidirect
48. #63978C22semidirect
49. #63971C22semidirect
60. #63958C22semidirect
61. #63911C22semidirect
62. C4×#626C22semidirect
63. #63897C22semidirect
64. #63884C22semidirect
65. #63880C22semidirect
66. #63867C22semidirect
67. #63853C22semidirect
68. #63850C22semidirect
94. C2×#884D3semidirect
97. C2×#877D3semidirect
268. #884C2×D3semidirect
271. #877C2×D3semidirect
718. C2×C32#540semidirect
879. C32C2×#540semidirect
945. C2×C3#5535semidirect
946. C2×C3#5615semidirect
996. C3C2×#5535semidirect
997. C3C2×#5615semidirect
1003. C2#10594206direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#640932
C2×C3×#8842
C2×C3×#8772
C2×#639782
C2×#639712
C2×#639582
C2×#639112
C2×C4×#6262
C2×#638972
C2×#638842
C2×#638802
C2×#638672
C2×#638532
C2×#638502
#105942062
C2×#56153
C2×#55353